Accurate S-Parameter Modeling and Material Characterization in Quasi-Optical Systems

Abstract

In the article, we present an analytical model of a beam interaction with a sample in a quasi-optical system suitable for high accuracy S-parameter prediction and material extraction. Instead of assuming a plane wave illumination of the sample, our model works with the fundamental Gaussian-beam mode (TEM <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$_{00}$</tex-math></inline-formula> ) incident on a homogeneous parallel sided slab with unknown refractive index. Using the Gaussian-beam coupling theory the sample’s parameters can be determined from the level of decoupling (defocusing) in the optical system caused by the sample’s presence. The complex transmission and reflection coefficients can both be calculated using the model for normal as well as for oblique incidence. Moreover, the model also allows for the inclusion of imperfections in the quasi-optical system such as frequency-dependent properties of source and detector antennas and nominal beam misalignment. We successfully test the model by measuring a high quality reference sample (refractive index independently characterized with an open resonator technique) in the frequency band 110–170 GHz. A comparison in terms of S-parameters and extracted refractive indices between our Gaussian-beam coupling model and a standard plane wave model is also given showing the relevance of our work.